Integrability of the sum of absolute values of blocks of the Fourier-Walsh series for functions of bounded variation

DOI10.1134/S0081543815060279zbMath1362.42057MaRDI QIDQ902076

Yuri V. Malykhin, Natalia Kholshchevnikova, Sergey A. Telyakovskii

Publication date: 7 January 2016

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

zbMATH Keywords

integrabilitybounded variationblocksWalsh series

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Absolute and strong summability (40F99)

Related Items (4)

On the boundedness of the \(L^{1}\)-norm of Walsh-Fejér kernels ⋮ Some properties of the Walsh-Nörlund means ⋮ Conditions under which the sums of absolute values of blocks in the Fourier-Walsh series for functions of bounded variation belong to spaces \(L^p\) ⋮ Conjugate transforms on dyadic group

Cites Work

• Series with respect to the Walsh system and their generalizations
• Refinement of the Dirichlet-Jordan and Young's theorems on Fourier series of functions of bounded variation
• On the Walsh Functions
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